Abstract
Oil-lubricated plastic gears enable significantly higher power transmission compared to dry-running gears. One of the most relevant damage mechanisms herein is tooth root breakage. Due to the high elasticity of thermoplastics, load-induced deflections strongly affect the tooth root stresses. In this work, a modified method for calculating the tooth root stresses is used to increase the accuracy of the bending strength calculation of plastic gears. Experimental results with steel-plastic spur gear pairings prove that load-induced deflections and dynamic tooth forces are not yet adequately considered in VDI 2736. In doing so, it was to some extent possible to validate and confirm the POM fatigue strength data in accordance with VDI 2736.
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References
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Acknowledgements
The authors would like to thank German Research Foundation (DFG, Deutsche Forschungsgemeinschaft, HO 1339/47-1) for their kind sponsorship of this research project focusing on the bending strength of thermoplastic gears. Furthermore, we kindly thank Werner Bauser GmbH (Siemensstr. 2; D‑78564 Wehingen) for the development and manufacturing of the injection molded test gears. We also thank DuPont™ for providing the raw material and support in conjunction with the manufacturing process of the test gears.
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Appendix
Appendix
1.1 Nomenclature
\(a_{\text{ACR}}\) | – | Auxiliary factor used to calculate\(Y_{\varepsilon ,\text{ACR}}\) | [9] |
\(b\) | mm | Face width | – |
\(c^{\prime}\) | N/(mm ⋅ µm) | Single stiffness | [2] |
\(c_{\gamma ,\text{ACR}}\) | N/(mm ⋅ µm) | Modified mesh stiffness according to ACORA | [9] |
\(\varepsilon _{\alpha }\) | – | Transverse contact ratio | [2] |
\(\varepsilon _{\alpha ,w}\) | – | Actual contact ratio | [8] |
\(F_{\text{t}}\) | N | Nominal tangential load | – |
\(K_{\text{v}}\) | – | Dynamic factor | [2] |
\(K_{\text{vT}}\) | – | Dynamic factor of the test gears | – |
\(m_{n}\) | mm | Normal module | – |
\(m_{\text{red}}\) | kg/mm | Relative mass of a gear pair | [2] |
\(n_{1}\) | \(\text{min}^{-1}\) | Rotation speed of pinion | [2] |
\(n_{\text{E1}}\) | \(\text{min}^{-1}\) | Resonance speed of pinion | [2] |
N | – | Resonance ratio | [2] |
\(N_{\text{L}}\) | – | Number of load cycles | – |
\(S_{\text{Fmin}}\) | – | Minimum required safety factor for tooth root stress | [1] |
\(\sigma _{\text{F0},\text{ACR}}\) | MPa | Nominal tooth root stress according to ACORARS | [9] |
\(\sigma _{F,\text{ACR}}\) | MPa | Tooth root stress according to ACORARS | – |
\(\sigma _{\text{FG}}\) | MPa | Maximum root strength | [1] |
\(\sigma _{\text{FG},\text{ACR}}\) | MPa | Maximum root strength according to ACORARS | – |
\(\sigma_{\text{FG},\text{VDI}\rightarrow \text{ACR}}\) | MPa | Maximum root strength derived from VDI 2736 | |
\(\sigma _{\text{FlimN}}\) | MPa | Fatigue strength under pulsating stress | [1] |
\(\vartheta _{\text{Fu{\ss}}}\) | °C | Root temperature | [1] |
\(Y_{\varepsilon ,\text{ACR}}\) | – | Modified contact ratio factor according to ACORA | [9] |
\(Y_{\varepsilon \text{T}}\) | – | Contact ratio factor of the test gears | – |
\(Y_{\beta }\) | – | Helix angle factor | [1] |
\(Y_{\text{Fa}}\) | – | Form factor (DIN 3990 Method C) | [2] |
\(Y_{\text{Sa}}\) | – | Stress correction factor (DIN 3990 Method C) | [2] |
\(Y_{\text{ST}}\) | – | Stress correction factor of the test gears | [1] |
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Hasl, C., Oster, P., Tobie, T. et al. Bending strength of oil-lubricated cylindrical plastic gears. Forsch Ingenieurwes 81, 349–355 (2017). https://doi.org/10.1007/s10010-017-0224-2
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DOI: https://doi.org/10.1007/s10010-017-0224-2